Question

A wheel on a skateboard has a diameter of 8 cm.
If the skateboard travels 12,560 cm, approximately how many times does the wheel rotate?

Write a verbal model to describe this situation.


Write an equation.


Solve the problem.

Answer 1

Given:

The diameter of the wheel on the skateboard is 8 cm

The skateboard travels 12560 cm

To find:

The no. of times the wheel will rotate

Solution:

The diameter, d = 8 cm

∴ The radius of the wheel, r = $\frac{Diameter}{2} = \frac{8}{2} = 4\: cm$

We know that the the distance covered by the wheel of the skateboard in 1 rotation will be equal to the circumference of the circle.

Let "n" be the required no. of rotations the wheel had made to cover 12,560 cm.

So, we can form the eq. as

The distance covered by the skateboard = n × Circumference of the wheel

⇒ 12,560 = n × 2πr

⇒ 12560 = n × 2 × $\frac{22}{7}$ × 4

⇒ n = $\frac{12560\: *\:7 }{2\:*\:22\:*\:4}$

⇒ n = $\frac{87920}{176}$

⇒ n = 499.54 ≈ 500

Thus, the wheel will rotate 500 times approximately.

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